Finite Group Databasebeta

C2×C4×#10587677 #17978852

order4352
automorphism?
homologyAbelianization (H1) = C23×C42 · Schur multiplier (H2) = C27×C42

Aliases

direct productC2×C4×#10587677

Splittings

FittingC22×C42×C17 ⋊ C4
SylowC17 ⋊ C2×C4×#117

Subgroups

subgroupG/H
centerC2×C42C2×#595
commutatorC2×C17C23×C42
FrattiniC22C24×#595
FittingC22×C42×C17C4
socleC23×C17C23×C4
prime radicalC24×D17C23
cosocleC22×D17C25
hypercenterC22×C42#595
hypocenterC17C2×C4×#117
LCSG ▷ C2×C17 ▷ C17
UCSC1 ◁ C2×C42 ◁ C22×C42

4462 conjugacy classes of subgroups.

Full subgroup data →

Presentation

transitive degreeμt(G) = 1088

Conjugacy classes & character table

416 conjugacy classes. The character table is too large to display.

GAP

Construct this group in GAP via the SmallGroups library:

gap> SmallGroup(4352, 1114096);